NAME

Statistics::LTU - An implementation of Linear Threshold Units

SYNOPSIS

    use Statistics::LTU;

    my $acr_ltu = new Statistics::LTU::ACR(3, 1);    # 3 attributes, scaled

    $ltu->train([1,3,2],  $LTU_PLUS);
    $ltu->train([-1,3,0], $LTU_MINUS);
    ...
    print "LTU looks like this:\n";
    $ltu->print;

    print "[1,5,2] is in class ";
    if ($ltu->test([1,5,2]) > $LTU_THRESHOLD) { print "PLUS" }
	                                 else { print "MINUS" };

    $ltu->save("ACR.saved") or die "Save failed!";
    $ltu2 = restore Statistics::LTU("ACR.saved");

EXPORTS

For readability, LTU.pm exports three scalar constants: $LTU_PLUS (+1), $LTU_MINUS (-1) and $LTU_THRESHOLD (0).

DESCRIPTION

Statistics::LTU defines methods for creating, destroying, training and testing Linear Threshold Units. A linear threshold unit is a 1-layer neural network, also called a perceptron. LTU's are used to learn classifications from examples.

An LTU learns to distinguish between two classes based on the data given to it. After training on a number of examples, the LTU can then be used to classify new (unseen) examples. Technically, LTU's learn to distinguish two classes by fitting a hyperplane between examples; if the examples have n features, the hyperplane will have n dimensions. In general, the LTU's weights will converge to a define the separating hyperplane.

The LTU.pm file defines an uninstantiable base class, LTU, and four other instantiable classes built on top of LTU. The four individual classes differs in the training rules used:

ACR - Absolute Correction Rule

TACR - Thermal Absolute Correction Rule (thermal annealing)

LMS - Least Mean Squares rule

RLS - Recursive Least Squares rule

Each of these training rules behaves somewhat differently. Exact details of how these work are beyond the scope of this document; see the additional documentation file (ltu.doc) for discussion.

SCALARS

$LTU_PLUS and $LTU_MINUS (+1 and -1, respectively) may be passed to the train method. $LTU_THRESHOLD (set to zero) may be used to compare values returned from the test method.

METHODS

Each LTU has the following methods:

new TYPE(n_features, scaling)

Creates an LTU of the given TYPE. TYPE must be one of:

Statistics::LTU::ACR,

Statistics::LTU::TACR,

Statistics::LTU::LMS,

Statistics::LTU::RLS.

n_features sets the number of attributes in the examples. If scaling is 1, the LTU will automatically scale the input features to the range (-1, +1). For example:

$ACR_ltu = new Statistics::LTU::ACR(5, 1);

creates an LTU that will train using the absolute correction rule. It will have 5 variables and scale features automatically.

copy

Copies the LTU and returns the copy.

destroy

Destroys the LTU (undefines its substructures). This method is kept for compatibility; it's probably sufficient simply to call undef($ltu).

print

Prints a human-readable description of the LTU, including the weights.

save(filename)

Saves the LTU to the file filename. All the weights and necessary permanent data are saved. Returns 1 if the LTU was saved successfully, else 0.

restore LTU(filename)

Static method. Creates and returns a new LTU from filename. The new LTU will be of the same type.

test(instance)

Tests the LTU on instance, the instance vector, which must be a reference to an array. Returns the raw (non-thresholded) result. A typical use of this is:

if ($ltu->test($instance) >= $LTU_PLUS) {
   # instance is in class 1
} else {
   # instance is in class 2
}

correctly_classifies(instance, realclass)

Tests the LTU against an instance vector instance, which must be a reference to an array. realclass must be a number. Returns 1 if the LTU classifies instance in the same class as realclass. Technically: Returns 1 iff instance is on the realclass side of the LTU's hyperplane.

weights

Returns a reference to a copy of the LTU's weights.

set_origin_restriction(orig)

Sets LTU's origin restriction to orig, which should be 1 or 0. If an LTU is origin-restricted, its hyperplane must pass through the origin (ie, so its intercept is zero). This is usually used for preference predicates, whose classifications must be symmetrical.

is_cycling(n)

Returns 1 if the LTU's weights seem to be cycling. This is a heuristic test, based on whether the LTU's weights have been pushed out in the past n training instances. See comments with the code.

version

Returns the version of the LTU implementation.

In addition to the methods above, each of the four classes of LTU defines a train method. The train method "trains" the LTU that an instance belongs in a particular class. For each train method, instance must be a reference to an array of numbers, and value must be a number. For convenience, two constants are defined: $LTU_PLUS and $LTU_MINUS, set to +1 and -1 respectively. These can be given as arguments to the train method. A typical train call looks like:

$ltu->train([1,3,-5], $Statistics_LTU_PLUS);

which trains the LTU that the instance vector (1,3,-5) should be in the PLUS class.

• For ACR: train(instance, value)

  Returns 1 iff the LTU already classified the instance correctly, else 0.

• For RLS: train(instance, value)

  Returns undef.

• For LMS: train(instance, value, rho)

  Returns 1 if the LTU already classified the instance correctly, else 0. Rho determines how much the weights are adjusted on each training instance. It must be a positive number.

• For TACR: train(instance, value, temperature, rate)

  Uses the thermal perceptron (absolute correction) rule to train the specified linear threshold unit on a particular instance_vector. The instance_vector is a vector of numbers; each number is one attribute. The desired_value should be either $LTU_PLUS (for positive instances) or $LTU_MINUS (for negative instances). The temperature and rate must be floating point numbers.

  This method returns 1 if the linear threshold unit already classified the instance correctly, otherwise it returns 0. The TACR rule only trains on instances that it does not already classify correctly.

AUTHOR

fawcett@nynexst.com (Tom Fawcett)

LTU.pm is based on a C implementation by James Callan at the University of Massachusetts. His version has been in use for a long time, is stable, and seems to be bug-free. This Perl module was created by Tom Fawcett, and any bugs you find were probably introduced in translation. Send bugs, comments and suggestions to fawcett@nynexst.com.

BUGS

None known. This Perl module has been moderately exercised but I don't guarantee anything.